MinT - Best Known (100, 100+133, s)-Nets in Base 4

Best Known (100, 100+133, s)-Nets in Base 4

(100, 100+133, 104)-Net over F₄ — Constructive and digital

Digital (100, 233, 104)-net over F₄, using

t-expansion [i] based on digital (73, 233, 104)-net over F₄, using
- net from sequence [i] based on digital (73, 103)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 73 and N(F) ≥ 104, using
    - F₆ from the tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(100, 100+133, 144)-Net over F₄ — Digital

Digital (100, 233, 144)-net over F₄, using

t-expansion [i] based on digital (91, 233, 144)-net over F₄, using
- net from sequence [i] based on digital (91, 143)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 91 and N(F) ≥ 144, using
    - Drinfeld modules of rank 1 [i]

(100, 100+133, 1053)-Net in Base 4 — Upper bound on s

There is no (100, 233, 1054)-net in base 4, because

1 times m-reduction [i] would yield (100, 232, 1054)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 47 957918 962988 179222 246806 386543 664057 325066 934466 719148 208948 870166 175499 115272 229586 899532 488887 817153 615910 227536 234604 009915 369060 687776 > 4²³² [i]